Measurements of the real part Z.sub.1 and the imaginary part Z.sub.2 of complex electromagnetic impedances Z=Z.sub.1 +jZ.sub.2 as a function of frequency and temperature are indispensible for the development and production of passive electronic components, e.g. of capacitors and coils. Furthermore, the knowledge of dielectric and magnetic material parameters is important for the development of materials or for production control. These parameters are also determined by impedance measurements.
In order to characterize an electronic component or a material, precise broad-band techniques for the determination of complex impedances are needed, which eleminates all errors from the measurement equipment including cables. As long as the wavelengths of the used electromagnetic waves are much larger than the cable lengths, the electrotechnical description will be sufficiently correct, i.e. each measurement arrangement may be considered as a linking of lumped elements. Above 1 MHz additional effects become noticeable, which are described with the help of transmission line theory. Within the framework of this theory one speaks more generally of transmission lines. (K Kupfmuller, Einfuhrung in die theoretische Elektrotechnik, Springer, 11th Edition, 1984, Chapter 5). At all discontinuities in a transmission line, current or voltage will be reflected and therefore multiple reflections between these discontinuities will occur. Therefore, current and voltage along a transmission line will change in contrast to the electrotechnical description. But also along homogeneous lines phase variations of current and voltage become noticeable. As the phase length of a line is proportional to the frequency, the influence of these effects will increase at higher frequencies. Therefore, these effects and the effects of multiple reflections have to be taken into account for the determination of the actual voltage-current ratio which defines the impedance.
Up to now there is no precise technique for the determination of complex impedances which works in the low frequency range from 0 to 10 MHz as well as up to file microwave region of some GHz. Therefore, one has to use different techniques for a broad-band determination of impedances. This requires a lot of time and equipment for preparing and carrying out the measurements. Furthermore, the known techniques have different disadvantages in the range above 10 MHz. In the following different measurement methods in the frequency range between 0 and 10 GHz are descibed as state of technology.
a) Impedance measurement by balancing a bridge, for example auto frequency bridges, transformer ratio bridges, autobalanced bridges, LCR-meters, impedance analyzers etc. (J. R. Macdonald, Impedance Spectroscopy, J. Wiley & Sons, 1987, 1st Edition, Chapter 3).
In general no phase variations and no multiple reflections are taken into account by balancing a bridge and therefore precise measurements can be carried out only up to about 10 MHz.
b) Measurement of transmission and reflection coefficients while taking into account the influence of the feeding lines by a calibration with 3 different standards. A summary of all the different techniques is given in: A Generalized Theory and New Calibration Procedures for Network Analyzer Self-Calibration, H. J. Eul and B. Schiek, IEEE Transactions on Microwave Theory and Techniques, Vol. 39, No. 4, April 1991.
Applying these techniques the reflection- and transmission-coefficients of a transmission path, in which a measurement cell with the unknown impedance is inserted, are measured for either possible signal directions, i.e. 4 complex values per measurement frequency. The influence of the feeding lines is eliminated using a 3 step procedure, the calibration. During the calibration, in the place of the measurement cell three different standards are connected in, succession to the feeding lines, and the reflection and transmission coefficients are measured. In addition to the time and equipment needed (bridges to split off reflected signals, reversal of signal flow) there are two principal disadvantages of these techniques which limit their application and accuracy. The used standards change their properties as a function of temperature in an unknown way, so that the influence of the feeding lines may be determined only at room temperature (this is not true for techniques which use different line-lengths for the calibration. But these are no broad-band techniques and they are not realizable in the frequency range discussed here because of the large wavelengths). Therefore, precise impedance measurements can be carried out only near room temperature. The influence of the measurement cell which contains the unknown impedance is only taken into account if the cell matches the impedance of the transmission line (the phase length of the measrement cell has to be determined, for example, by an additional transmission measurement). This is an idealizing assumption which is difficult to realize and which limits the accuracy of the impedance measurement and the possible geometries of measurement cells.
c) Measurement of reflection coefficients using impedance analyzers or network analyzers (e.g. sample as termination of a coaxial line, see: A. Rost, Messung dielektrischer Stoffeigenschaften, Vieweg, 1978, 1. Edition, Chapter 4.3).
These techniques are not applicable below 1 MHz and they do not allow the resolution of loss tangents Z.sub.1 /Z.sub.2 with values smaller than 10.sup.-1, in an ideal case smaller than 10.sup.-2 (see e.g. N.-E. Belhadj-Tahar, Thede doctorat de l'Universite Pierre et Marie Curie, Paris IV, 1986). The influence of the feeding line is determined as described in b) using three different standards. Therefore, the same limitations are valid for temperature dependent measurements.